Book:Gert K. Pedersen/Analysis Now/Second Edition

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Gert K. Pedersen: Analysis Now (2nd Edition)

Published $1995$, Springer

ISBN 978-0387967882.


Subject Matter

Functional Analysis

Contents

Preface

Chapter 1: General Topology
1.1 Ordered Sets
1.2 Topology
1.3 Convergence
1.4 Continuity
1.5 Separation
1.6 Compactness
1.7 Local Compactness
Chapter 2: Banach Spaces
2.1 Normed Spaces
2.2 Category
2.3 Dual Spaces
2.4 Seminormed Spaces
2.5 $w^*$-compactness
Chapter 3: Hilbert Spaces
3.1 Inner products
3.2 Operators on Hilbert Space
3.3 Compact Operators
3.4 The Trace
Chapter 4: Spectral Theory
4.1 Banach Algebras
4.2 The Gelfand Transform
4.3 Function Algebras
4.4 The Spectral Theorem, I
4.5 The Spectral Theorem, II
4.6 Operator Algebra
4.7 Maximal Commutative Algebras
Chapter 5: Unbounded Operators
5.1 Domains, Extensions and Graphs
5.2 The Cayley Transform
5.3 Unlimited Spectral Theory
Chapter 6: Integration Theory
6.1 Radon Integrals
6.2 Measurability
6.3 Measures
6.4 $L^p$ spaces
6.5 Duality theory
6.6 Product Intergrals

Bibliography

List of Symbols

Index